After coming through the youth system at Partizan, Brežančić signed his first professional contract with the club on 1 June 2007, penning a five-year deal.
In January 2009, Brežančić returned to Partizan and made seven league appearances until the end of the 2008–09 season, as the club won the title.
[3] He made his official debut for the team in a 3–1 away league win over De Graafschap on 12 September 2015, scoring the opener early in the game.
On 11 November 2018, Brežančić made his La Liga debut in a 2–1 away loss to Alavés, replacing injured Pablo Insua.
[7] He made 16 appearances across all competitions in his first season back at the club, scoring a goal in a 2–2 away league draw against Napredak Kruševac.